{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Construction of the interpolation weights is a relatively slow process. If you want to call this many times with the same xi (but possibly varying yi or x) you should use the class "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "BarycentricInterpolator",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.interpolate._polyint:BarycentricInterpolator"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". This is what this function uses internally."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "y",
              "annotation": "scalar or array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Interpolated values. Shape is determined by replacing the interpolation axis in the original array with the shape of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "x"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Convenience function for barycentric interpolation."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "xi",
              "annotation": "array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "1-D array of x coordinates of the points the polynomial should pass through"
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "yi",
              "annotation": "array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The y coordinates of the points the polynomial should pass through."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "x",
              "annotation": "scalar or array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Point or points at which to evaluate the interpolant."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "axis",
              "annotation": "int, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Axis in the "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "yi"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " array corresponding to the x-coordinate values."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "der",
              "annotation": "int or list or None, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "How many derivatives to evaluate, or None for all potentially nonzero derivatives (that is, a number equal to the number of points), or a list of derivatives to evaluate. This number includes the function value as the '0th' derivative."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "rng",
              "annotation": "`numpy.random.Generator`, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Pseudorandom number generator state. When "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "rng"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is None, a new "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "numpy.random.Generator",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": "numpy",
                        "version": "*",
                        "kind": "api",
                        "path": "numpy.random._generator:Generator"
                      },
                      "kind": "module"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is created using entropy from the operating system. Types other than "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "numpy.random.Generator",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": "numpy",
                        "version": "*",
                        "kind": "api",
                        "path": "numpy.random._generator:Generator"
                      },
                      "kind": "module"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " are passed to "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "numpy.random.default_rng",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": "numpy",
                        "version": "*",
                        "kind": "api",
                        "path": "numpy.random:default_rng"
                      },
                      "kind": "module"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " to instantiate a "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "Generator"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Constructs a polynomial that passes through a given set of points, then evaluates the polynomial. For reasons of numerical stability, this function does not compute the coefficients of the polynomial."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "This function uses a \"barycentric interpolation\" method that treats the problem as a special case of rational function interpolation. This algorithm is quite stable, numerically, but even in a world of exact computation, unless the "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "x"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " coordinates are chosen very carefully - Chebyshev zeros (e.g., cos(i*pi/n)) are a good choice - polynomial interpolation itself is a very ill-conditioned process due to the Runge phenomenon."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": "/scipy/interpolate/_polyint.py",
  "item_line": 952,
  "item_type": "function",
  "aliases": [
    "scipy.interpolate.barycentric_interpolate"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "We can interpolate 2D observed data using barycentric interpolation:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.interpolate import barycentric_interpolate\nx_observed = np.linspace(0.0, 10.0, 11)\ny_observed = np.sin(x_observed)\nx = np.linspace(min(x_observed), max(x_observed), num=100)\ny = barycentric_interpolate(x_observed, y_observed, x)\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "plt.plot(x_observed, y_observed, \"o\", label=\"observation\")\nplt.plot(x, y, label=\"barycentric interpolation\")\nplt.legend()\n",
        "execution_status": "failure"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "plt.show()\n",
        "execution_status": "success"
      },
      {
        "__type": "Figure",
        "__tag": 4024,
        "value": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "scipy",
          "version": "1.17.1",
          "kind": "assets",
          "path": "fig-7374449dfe5c28c3.png"
        }
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "BarycentricInterpolator",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.interpolate._polyint:BarycentricInterpolator"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Barycentric interpolator"
            }
          ]
        }
      ],
      "type": null
    }
  ],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "xi",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "yi",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "x",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "axis",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "0"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "der",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "KEYWORD_ONLY",
        "default": "0"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "rng",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "KEYWORD_ONLY",
        "default": "None"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "barycentric_interpolate"
  },
  "references": null,
  "qa": "scipy.interpolate._polyint:barycentric_interpolate",
  "arbitrary": [],
  "local_refs": [
    "axis",
    "der",
    "rng",
    "x",
    "xi",
    "y",
    "yi"
  ]
}